DYNAMICS Engr 80
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Date Created: 09/12/15
VOLUME 80 NUMBER 1 PHYSICAL REVIEW LETTERS 5 JANUARY 1998 Wetting near Triple Points K G Sukhatme I E Rutledge and P Taborek Department ofPhysics andAstronomy University ofCalifornia Irvine California 926974575 Received 14 August 1997 The quartz microbalance technique has been used to study the coverage of argon and methane lms in the vicinity of the bulk triple point In contrast to previous measurements close to the triple point the discontinuities in the coverage indicate rstorder surface phase transitions A thermodynamic model shows that argon forms a layered solidliquid lm in a range around the triple point but is liquid both above and below this range Methane lms make a transition directly from solid to liquid These observations are examples of the rich phase behavior near bulk triple points predicted by Pandit and Fisher Phys Rev Lett 51 772 1983 PACS numbers 6835Rh 6845Da 6845Gd At the triple point of a one component system bulk solid liquid and vapor can coexist but even a small thermodynamic perturbation will break this degeneracy The interfaces at the substrate and the vapor of an ad sorbed lm provide such a perturbation For this rea son the phase of the lm is not uniquely determined by the bulk phase diagram The consequences of inter facial effects are surprisingly subtle and determine phe nomena such as nonwetting of solid lms l2 surface melting 3 nucleation and triplepointinduced wetting 478 and dewetting 9 Pandit and Fisher 10 have discussed a number of possible surface phase diagrams They show that typically surface phases are separated by rstorder phase transitions at temperatures distinct from the bulk triple temperature T Nevertheless experiments near solidliquidvapor triple points have never revealed transitions except at T Previous experiments have re lied on two types of techniques The rst utilizes thermo dynamic measurements on exfoliated graphite substrates ll Recently it has become clear that multilayer ad sorption on these substrates is always accompanied by capillary condensation so it is very dif cult to determine surface phases near coexistence 12 Another class of experiments including the one reported here utilizes mi crobalances 5 7913 which do not suffer from this com plication All previous microbalance experiments have identi ed a single particularly simple type of triplepoint wetting scenario in which a thin liquidlike lm is stabi lized on the substrate below T and the thickness d di verges as a power law d t with t T 7 TT The exponent n is approximately 71 3 which re ects the fact that the chemical potential of the liquid below T is larger than the chemical potential at solidvapor co existence by an amount proportional to t This must be compensated by the decrease in the chemical potential due to the van der Waals interaction with the substrate which is proportional to 1d3 The experiments we de scribe below provide evidence for a distinctly different type of surface phase behavior In particular for Ar on gold we nd that near bulk coexistence a layered solid liquid lm structure is stabilized in an approximately 3 K 0031 90079880112941500 SOO3190079704948X interval which brackets T The layered phase melts for temperatures both above and surprisingly below this in terval The thickness of the low temperature liquid lm obeys a power law in it For methane on gold lms below T are always solid and the thickness is almost in dependent of t The quartz microbalance technique used to monitor the adsorbed coverage is conventional 5 779 Adsorption takes place on the gold electrodes of the microbalance which were used as received from the manufacturer The main experimental challenge in these studies is to provide a uniform thermal environment The microbalance was mounted in a cell inside two concentric radiation shields The cell and the inner shield were made of goldplated copper to minimize thermal gradients Our thermometers were calibrated by measuring the saturated vapor pressure to locate the bulk triple point using a cell connected to a heated ll line The data reported here however were obtained using a cell which was loaded with gas at room temperature and then sealed to entirely eliminate the heated ll line The amount of gas was suf cient to ensure that several mm3 of bulk phase formed near T The primary data of our experiment consist of the frequency shift of the microbalance as a function of temperature data for Ar and CH4 are shown in Figs 1 and 2 where the frequency shift has been converted to thickness in layers Data were collected by changing the temperature of the cell by approximately 20 mK and waiting for the microbalance frequency to settle As has been noted previously 8 we found that the time constant for mass transport in the cell was surprisingly long and more than 24 h of settling time was typically required per data point Figure 1 shows data for Ar as a function of t For t gt 002 corresponding to temperature more than 16 K above the triple temperature 8331 K there are approximately 32 layers of adsorbed liquid39 this value is determined by the competition between van der Waals forces which tend to thicken the lm and gravity which tends to thin it At low temperatures eg t 7006 or 5 K below T the lm is approximately 5 layers thick 1997 The American Physical Society 129 VOLUME80NUMBER1 PHYSICAL REVIEW LETTERS 5JANUARY 1998 45 50 40 I 0 45 CH4Gold 39 39 39 ArGold 39 39 3 Experiment 35 39 Experiment 39 40 30 39 35 I 5 3 I lt3 Iquot d I o 6 20 13 d 25 Po 3 I A U 1539 11 20 I J l I o J 9 A A m g 0 39 55 quot0quot 7 oo14 oo1 oooe 1o 0 V I I I I I I I I 5 I I I I I 003 001 001 003 005 t FIG 1 The lm thickness in layers d as a function of reduced temperature I for argon on gold At high temperature the lm is liquid and the thickness is independent of temperature At t 002 there is a rstorder transition to a layered state which persists until I 0007 where the lm again becomes liquid The transition at t 0007 is hysteretic see inset squares are cooling and triangles are heating As can be seen in Fig l the transition from the thick high temperature state to the thin low temperature lm is not a smooth function of temperature There are two signi cant temperatures in addition to TI at t 0007 there is a small hysteretic step and a change in slope and at t 002 there is a discontinuity The thermodynamic model discussed below identi es the region 0007 lt t lt 002 as a layered phase with solid adjacent to the substrate and a liquid layer on top At both boundaries of this region there is a rstorder transition to a lm which is entirely liquid At high temperatures the lm is a wetting liquid lm with a thickness that is essentially independent of temperature while at low temperature the liquid lm thickness has a power law dependence on t with an exponent of 038 The layered lm thickness for 0007 lt t lt 0 obeys a power law dependence on t with an exponent of 028 Figure 2 shows that the temperature dependence of the lm thickness for CH4 is distinctly different from Ar Above TI 9068 K the lm has a constant temperature independent thickness of approximately 47 layers and shows no evidence of any phase transitions 0005 0003 0001 0001 0003 0005 t FIG 2 Film thickness d vs reduced temperature I for methane on gold Note the nite slope of dt at t 0 d vs I is smooth outside the narrow t range shown Arrows show the direction of the temperature change in the hysteric region layers It is noteworthy that in CH4 both the bulk phase transition and the lm thinning are hysteretic with a width of approximately 010 K while in Ar the hysteresis in the bulk transition was undetectable For CH4 below TI the lm thickness is a smooth slowly varying function of t having a nite slope at t 0 Pandit and Fisher 10 pointed out that the stability of various surface phases depends critically on the relative size of the surface tensions 071 am 03951 am and am where l liquid 5 solid v vapor and w wall and that a large number of surface phase transitions are possible in the vicinity of the triple point Pettersen Lysek and Goodstein 14 have constructed a simple phenomenological model in which the lm is regarded as a slab or slabs of bulk phase with the surface tension van der Waals potentials and other effects treated as perturbations We have used this type of model to interpret our data The basis of the method is to write the grand free energy 201 T z for a lm of arbitrary thickness z and minimize Q with respect to z Near the triple point there are three ee energies ll 5 and May for the liquid solid and layered lm which need to be considered the stable phase is of course the one with the lowest value of 0 For example the free energy of the layered phase for arbitrary values of the thickness At the triple point the lm thickness abruptly thins to 21 I of the liquid and solid slabs z and ZS is ACg W AC QlayL9TZlazs ps 100752 1012 le AC W pl m mm mTzz psu MsTzs 0514 0 51 0111 mghplzl psZs 9 S where p are the densities LI39T are the bulk chemical I proportional to u LI39T express the cost of forming potentials and AC are differences of van der Waals C3 coef cients for the various bulk phases The terms 130 a phase away from bulk coexistence The term con taining the surface tensions 071 accounts for the energy VOLUME 80 NUMBER 1 PHYSICAL REVIEW LETTERS 5 JANUARY 1998 required to form solidwall solidliquid and liquidvapor interfaces The term proportional to mgh accounts for the gravitational potential energy of the lm while the last term proportional to 8 accounts for the strain energy in the solid part of the lm 12 Similar terms appear in I and 1 See Ref 1415 for further details Equation 1 and its analog for IS and Q can be nu merically minimized with respect to the zi The equi librium Q the surface phase and the lm thicknesses are then determined by the lowest lying branch at each temperature The relative positions of the three branches are determined by the magnitudes of the surface tensions Figure 3 shows three different orderings of the ee en ergies with u the bulk coexistence value The order ings correspond to different sequences of surface phase transitions near T The qualitative behavior of each ee energy branch is independent of the values of the parame ters The single phase branches have essentially constant values of Q as long as the corresponding bulk phase is stable with a cusplike rise at the triple point where the bulk phase becomes metastable hay is V shaped with a sharp minimum at T Figure 3a corresponds to the Ar surface phase diagram obtained from the data in Fig l with a high and low temperature liquid phase separated by a layered phase near T Figure 3b shows a direct tran sition from liquid to solid at a temperature very close to T which we believe is the case for CH4 Figure 3c il lustrates the triplepoint wetting scenario inferred om all previous experiments in which liquid lms coexist with bulk solid over a wide range of temperature To compare the model with the experiments the z given by the equilibrium 0 can be compared to the data in Figs 1 and 2 This requires numerical values for the pa rameters in the ee energy of Eq 1 Although the den sities 16 van der Waals coef cients l7 bulk chemical potentials and 03911 are known 05W 03951 and the elas tic strain parameter 8 are not If 05W 051 and 8 are treated as temperature independent tting parameters we nd that the model cannot reproduce the features we ob serve at t 0007 and 002 Both the elastic constants which determine 8 and the surface tensions are in fact temperature dependent If we include a linear coef cient of temperature variation for 039s and 8 as additional tting parameters we obtain qualitative agreement between the model and the data The parameters resulting from the tting procedure are physically reasonable Details will be given elsewhere 15 Figure 4 shows the coverage as a 1nction of temperature for Ar on Au The model accu rately reproduces the positions of the discontinuities In the liquid phase the model predicts that the lm thick ness obeys a power law with an exponent of 034 and an exponent of 027 in the layered phase in reasonable agreement with the data A similar analysis of the CH4 data shows that the ee energy diagrams for this case look qualitatively like Fig 3b The fact that the lm thickness is independent Liquid Solid Layered FIG 3 Qualitative behavior of I for a liquid solid line solid dotted line and layered dashed line lm as a function of reduced temperature The relative ordering of the free energies is determined by the surface tensions In a the layered state has the lowest free energy in a range of temperatures at about T while the liquid lm is the stable phase outside this range This corresponds to the case of Ar on Au In b the liquid lm is stable above T while the solid lm is stable below T this corresponds to the observed behavior of CH on Au In c the liquid lm has the lowest free energy over a wide temperature range at about T This case describes previously observed triplepoint wetting with no transitions for T T and smooth powerlaw dependence of the lm thickness of temperature above T implies that the liquid branch lies below both the solid and layered branch in this tempera ture range The smooth behavior of the thickness below T as well as the nondivergent temperature dependence of the thickness suggests that the lm is entirely solid As Fig 3b shows the surface transition can lie extremely close to T even for substantial offsets in the 0 vs t curves In this scenario the layered state is never stable l3l
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